Simplify i^7*7

$i^{7} \cdot 7$

Step 1

Rewrite $i^{7}$ as $i^{4} (i^{2} \cdot i)$ .

Factor out $i^{4}$ .

$i^{4} i^{3} \cdot 7$

Factor out $i^{2}$ .

$i^{4} (i^{2} \cdot i) \cdot 7$

$i^{4} (i^{2} \cdot i) \cdot 7$

Step 2

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

${(i^{2})}^{2} (i^{2} \cdot i) \cdot 7$

Rewrite $i^{2}$ as $- 1$ .

${(- 1)}^{2} (i^{2} \cdot i) \cdot 7$

Raise $- 1$ to the power of $2$ .

$1 (i^{2} \cdot i) \cdot 7$

$1 (i^{2} \cdot i) \cdot 7$

Step 3

Multiply $i^{2} \cdot i$ by $1$ .

$i^{2} \cdot i \cdot 7$

Step 4

Rewrite $i^{2}$ as $- 1$ .

$- 1 \cdot i \cdot 7$

Step 5

Rewrite $- 1 i$ as $- i$ .

$- i \cdot 7$

Step 6

Multiply $7$ by $- 1$ .

$- 7 i$

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